Heavenly Stems & Earthly Branches
Summary
Tiangan Dizhi, shortened to Ganzhi, consists of two ordered sets: ten Heavenly Stems and twelve Earthly Branches. Advancing both sets together produces Jia Zi, Yi Chou, Bing Yin and the remaining pairs through Gui Hai: a cycle of sixty. Years, months, days and two-hour periods can all carry a Ganzhi designation, but each requires its own timing rules.
Read this handbook in sequence, or jump to the individual stems and branches, the sixty-pair cycle, or calendar boundaries. Calendar facts, traditional phase classifications and conventions used in divination are explained in their respective contexts.
On this page
One sequence system, several uses
The two sequences and their pairing
The ten stems are Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui. The twelve branches are Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai. A designation places the stem first and the branch second: Jia Zi, pronounced jiǎ zǐ, is the standard order, not Zi Jia.
After Gui, the stem sequence returns to Jia; after Hai, the branch sequence returns to Zi. These restarts need not happen together. Gui You is followed by Jia Xu, then Yi Hai and Bing Zi. The complete sequence can be checked against the Hong Kong Observatory's table.
Ganzhi, the zodiac, Wuxing and Bazi are not interchangeable names. Ganzhi supplies the ordered symbols; the zodiac associates an animal with each branch; Wuxing assigns traditional phase classifications; Bazi uses four pairs for year, month, day and hour. Knowing that a year is a Dragon year identifies its Chen branch, but neither its stem nor a person's full Bazi chart.
What the historical evidence establishes
The Central Weather Administration's explanation of the cycle describes a complete Ganzhi day-counting system in Shang oracle-bone records. The transmitted Mu Shi chapter of the Shang Shu also uses Jia Zi to identify a day. These sources establish early day designation; they do not identify a securely proven single inventor or invention year.
Year, month, day and hour applications should not be assumed to have appeared together. Evidence for Shang day counting is not evidence that Shang Bazi calculations already matched today's four-pillar methods. Later texts such as Wu Xing Da Yi recount a traditional origin story involving Da Nao. An origin narrative and an excavated inscription belong to different evidential categories.
The animal correspondences have their own history. The Hong Kong Observatory's zodiac page states that zodiac year designation was already used in the first century CE and lists the animal–branch associations. It does not claim that the Ganzhi sequences were originally derived from twelve animals.
Ten stems and twelve branches, individually explained
Select a tile to look up a fact, without an AI request. Hours use common modern clock equivalents; hidden stems list members, not proportions.
Complete reference table
| Name | Polarity · phase | Hidden stems | Zodiac animal | Common clock-time range |
|---|---|---|---|---|
| Jiajiǎ | Yang · Wood | — | — | — |
| Yiyǐ | Yin · Wood | — | — | — |
| Bingbǐng | Yang · Fire | — | — | — |
| Dingdīng | Yin · Fire | — | — | — |
| Wuwù | Yang · Earth | — | — | — |
| Jijǐ | Yin · Earth | — | — | — |
| Genggēng | Yang · Metal | — | — | — |
| Xinxīn | Yin · Metal | — | — | — |
| Renrén | Yang · Water | — | — | — |
| Guiguǐ | Yin · Water | — | — | — |
| Zizǐ | Yang · Water | Gui | Rat | 23:00–01:00 |
| Chouchǒu | Yin · Earth | Ji · Gui · Xin | Ox | 01:00–03:00 |
| Yinyín | Yang · Wood | Jia · Bing · Wu | Tiger | 03:00–05:00 |
| Maomǎo | Yin · Wood | Yi | Rabbit | 05:00–07:00 |
| Chenchén | Yang · Earth | Wu · Yi · Gui | Dragon | 07:00–09:00 |
| Sisì | Yin · Fire | Bing · Geng · Wu | Snake | 09:00–11:00 |
| Wuwǔ | Yang · Fire | Ding · Ji | Horse | 11:00–13:00 |
| Weiwèi | Yin · Earth | Ji · Ding · Yi | Goat | 13:00–15:00 |
| Shenshēn | Yang · Metal | Geng · Ren · Wu | Monkey | 15:00–17:00 |
| Youyǒu | Yin · Metal | Xin | Rooster | 17:00–19:00 |
| Xuxū | Yang · Earth | Wu · Xin · Ding | Dog | 19:00–21:00 |
| Haihài | Yin · Water | Ren · Jia | Pig | 21:00–23:00 |
The yin–yang, phase, direction and imagery below describe traditional classifications. Jia, Bing, Wu, Geng and Ren are yang stems; Yi, Ding, Ji, Xin and Gui are yin stems. Zi, Yin, Chen, Wu, Shen and Xu are yang branches; the remaining six branches are yin. Polarity does not measure gender, goodness or personal ability. Trees, lamps, stars and rivers are explanatory metaphors, not findings about personality, occupation or real outcomes. Consult Wu Xing Da Yi, volume 2 for phase and seasonal correspondences and San Ming Tong Hui, volume 2 for stem polarity and imagery.
The ten stems, explained · 10
Jia · Yang Wood and firm-wood imagery
Jia, jiǎ, is the first stem, classified as yang Wood. Its five-combination partner is Ji. In a sequence it identifies a position; in a phase relationship it carries a Wood classification. Jia Zi and Jia Wu therefore share a stem but not a branch.
A large tree or a structural beam can help someone remember Jia's firm-Wood imagery. The earliest written form is a separate question requiring paleographic evidence. San Ming Tong Hui also invokes thunder and dragons when discussing Jia, giving one symbol several metaphorical paths. A useful first exercise is to identify Jia–Ji as a stem combination and Metal's control of Wood in Jia–Geng, naming the particular relation being used.
Yi · Yin Wood and flexible-wood imagery
Yi, yǐ, is the second stem, yin Wood, combining with Geng. Jia and Yi share a phase but cannot be exchanged in rules that distinguish polarity. Yi Si is a valid cycle pair; Yi Wu is not, because Yi and the branch Wu occupy different parity classes.
Flowers and vines are familiar flexible-Wood metaphors; older discussions also use wind and trees. Flexible-Wood imagery, polarity and seasonal strength are related but separate topics. An assessment of Yi's strength adds season and other relationships. After looking up yin Wood, continue with the contextual rules of the system being used.
Bing · Yang Fire and illumination
Bing, bǐng, is the third stem, yang Fire, combining with Xin. The Sun, illumination and furnace work appear as traditional imagery, emphasizing light, expression and refinement respectively.
Month derivation offers a concrete exercise. In a Jia or Ji year, the Yin month starts with Bing, making Bing Yin; the following months are Ding Mao and Wu Chen. Bing comes from the year-stem lookup rule. It supplies both the stem of the Yin month and the starting point for deriving the remaining months in order.
Ding · Yin Fire, lamps and stars
Ding, dīng, is the fourth stem, yin Fire, combining with Ren. San Ming Tong Hui uses both lamplight and stars, offering two imagery paths for the same symbol.
Bing and Ding are both Fire but differ in polarity. With Jia as the day-stem reference, both are generated by Wood: Bing receives Shishen, or Eating God, while Ding receives Shangguan, or Hurting Officer. The distinction comes from generation plus polarity. Ding–Ren is also a stem combination; a further Wood transformation interpretation adds the seasonal and contextual conditions of the chosen tradition.
Wu · Yang Earth, center and seasonal transitions
Wu, wù, is the fifth stem, yang Earth, combining with Gui. It is distinct from the branch Wu, pronounced wǔ, and from Xu, pronounced xū. In Wu Chen, stem and branch both have an Earth classification, but remain separate fields.
Earth's central position answers a question about direction. Its associations with late summer or the ends of the four seasons answer a question about seasonal correspondence. Wu Xing Da Yi, volume 1 contains these different formulations. Separate direction and season fields preserve Earth's positions on both axes. Assigning numerical strength weights would require an additional, explicitly defined rule.
Ji · Yin Earth and derivation groups
Ji, jǐ, is the sixth stem, yin Earth, combining with Jia. Its written form is easily confused with other similar-looking characters, including the branch Si. Checking the symbol itself is especially important when reading electronic transcriptions of older texts.
Cultivated soil is a familiar memory image; traditional discussions also use clouds and harmonizing qi. Ji shares Jia's group in both the Five Tigers month rule and the Five Rats hour rule. A Jia or Ji year starts with Bing Yin month, while a Jia or Ji day starts with Jia Zi hour. The shared Jia–Ji group is worth remembering alongside the two different starting stems.
Geng · Yang Metal and relative relationships
Geng, gēng, is the seventh stem, yang Metal, combining with Yi. Metal tools and cutting implements are useful firm-Metal images. Different traditional passages also use wind, frost or the Moon, emphasizing different aspects of the symbol.
Geng and Jia are both yang, but Metal controls Wood. Under the Ten Gods convention below, Jia identifies Geng as Qisha, or Seven Killings. Reverse the reference and Geng identifies Jia as Piancai, or Indirect Wealth: Wood is now the phase controlled by the reference Metal. The same two stems receive different relationship names when the day-stem reference changes.
Xin · Yin Metal and the officer reference
Xin, xīn, is the eighth stem, yin Metal, combining with Bing. Jewels are a common refined-Metal metaphor, while frost is another traditional image. Reading Xin alongside Geng helps retain both their shared Metal classification and their different polarity imagery.
For a Jia day-stem reference, Xin is the opposite-polarity Metal that controls Wood, receiving the name Zhengguan, or Direct Officer. Geng has the same polarity as Jia and receives Qisha instead. Xin also appears as a hidden stem in Chou, You and Xu. Those branches differ in principal phase, season and other hidden members; the presence of Xin does not make all three interchangeable.
Ren · Yang Water and flowing-water imagery
Ren, rén, is the ninth stem, yang Water, combining with Ding. Rivers and large bodies of water emphasize movement or extent; other traditional images include clouds and autumn dew. Ren and Gui share Water, with yang and yin distinguishing the pair.
Ren is the principal hidden stem of Hai and also appears among Shen's hidden stems. The statement that Shen contains Ren records membership in the selected table. It does not turn Shen into a Water branch: Shen's principal phase remains Metal. Keep the branch's principal phase separate from the complete collection of its hidden stems before counting or interpreting either.
Gui · Yin Water and the final stem position
Gui, guǐ, is the tenth stem, yin Water, combining with Wu. Rain, dew and springs are traditional memory images, offering a comparison with Ren's flowing-water imagery. Gui also occupies the final position of the ten-stem sequence.
After Gui comes Jia, but the branch sequence continues independently. Gui You is therefore followed by Jia Xu, not Jia Zi. Zi's hidden Gui also provides a useful test of two polarity fields: Zi is a yang branch and Gui a yin stem. There is no contradiction because the labels refer to different objects. Do not change the branch's polarity to make it match its hidden member.
How to read the branch entries
The following entries state this guide's Ziping hidden-stem membership table, placing the principal stem first without assigning percentages to the remaining order. The members agree with the hidden-stem verse in this electronic Yuan Hai Zi Ping. That page carries a source-verification warning, however, and cannot alone establish the exact wording of a particular historical edition. The four Earth branches can also be cross-checked against the mixed-qi discussion in San Ming Tong Hui, Siku Quanshu version, volume 5. The complete table here is an explicit teaching convention, not a claim that every historical version agrees.
Traditional allocations of ruling qi to days within a month, sometimes discussed as Renyuan Sishi, are a separate matter. Finding a stem in such a monthly allocation does not automatically add it to a hidden-stem membership list.
The time ranges use the Observatory's usual modern clock correspondences. Include the start and exclude the end of each range. Seasonal and directional associations belong to a traditional Northern Hemisphere calendrical framework; they do not describe the actual weather everywhere on Earth.
The twelve branches, explained · 12
Zi · Yang Water and the midnight-spanning hour
Zi, zǐ, is the first branch: yang, principal phase Water, zodiac Rat, 23:00–01:00, with hidden Gui. It occupies the northern position among the four cardinal branches and corresponds to midwinter in the seasonal sequence.
Zi combines with Chou, clashes with Wu and joins Shen and Chen in the Water trine. Its most common practical complication is midnight: an hour branch may remain Zi while the day pillar changes under the selected convention. Separating “which two-hour period?” from “which day?” prevents a simple clock table from being used to decide the day boundary for every charting tradition.
Chou · Yin Earth, late winter and Metal storage
Chou, chǒu, is the second branch: yin, principal phase Earth, zodiac Ox, 01:00–03:00, with hidden Ji, Gui and Xin. It corresponds to late winter and belongs to the four Earth branches with Chen, Xu and Wei.
Chou combines with Zi, clashes with Wei and participates in the Si–You–Chou Metal trine. Calling Chou a Metal storehouse refers to its storage position in that framework; it does not change Chou's principal phase to Metal. Its hidden Water and Metal members are also part of what distinguishes it from Wei, despite their shared Earth classification.
Yin · Yang Wood and the solar-month starting point
Yin, yín, is the third branch: yang, principal phase Wood, zodiac Tiger, 03:00–05:00, with hidden Jia, Bing and Wu. In this guide's Ziping convention, the Yin month begins at the Lichun instant and is followed by Mao.
Yin combines with Hai and clashes with Shen. It belongs both to the spring seasonal group Yin–Mao–Chen and to the Fire trine Yin–Wu–Xu. The latter does not permanently replace its principal Wood phase with Fire. The label growth branch also needs a phase or stem reference: Yin is not the Changsheng position for every day stem merely because it belongs to a group sometimes called the four growth branches.
Mao · Yin Wood, east and midspring
Mao, mǎo, is the fourth branch: yin, principal phase Wood, zodiac Rabbit, 05:00–07:00, with hidden Yi. It corresponds to the east among the cardinal branches and to midspring in the seasonal sequence.
Mao combines with Xu, clashes with You and joins Hai and Wei in the Wood trine. It also forms the Zi–Mao relation in the punishment table below. With Yi as its sole hidden stem, Mao is a useful single-member example for learning that table. Its combination partner, clash partner and group members can then be read separately in the relationship tables.
Chen · Yang Earth, late spring and Water storage
Chen, chén, is the fifth branch: yang, principal phase Earth, zodiac Dragon, 07:00–09:00, with hidden Wu, Yi and Gui. It corresponds to late spring and completes the eastern seasonal group with Yin and Mao.
Chen combines with You, clashes with Xu and joins Shen and Zi in the Water trine. “Chen is a Water storehouse” describes its storage position in that Water grouping. “Chen's principal phase is Earth” describes a branch attribute. “Chen contains Gui” describes hidden-stem membership. The three statements can coexist because none is a replacement definition for the other two.
Si · Yin Fire and overlapping relations
Si, sì, is the sixth branch: yin, principal phase Fire, zodiac Snake, 09:00–11:00, with hidden Bing, Geng and Wu. Its solar-term month begins at Lixia, and it opens the Si–Wu–Wei summer group.
Si combines with Shen while also appearing with Shen in the Yin–Si–Shen punishment sequence. It clashes with Hai and belongs to the Si–You–Chou Metal trine. This illustrates overlapping tables: combination and punishment can both be recorded, with their interpretation depending on further conditions. Hidden Geng and the Metal trine also belong to separate membership and relationship tables.
Wu · Yang Fire, south and midsummer
Wu, wǔ, is the seventh branch: yang, principal phase Fire, zodiac Horse, 11:00–13:00, with hidden Ding and Ji. It corresponds to the south and midsummer. Its pronunciation differs from the stem Wu, wù.
Wu clashes with Zi, combines with Wei and joins Yin and Xu in the Fire trine. Not every cardinal branch has just one hidden stem: Wu has Ding and Ji, whereas Zi, Mao and You each have one member in this guide's table. Check each branch rather than guessing the number of hidden stems from a group name.
Wei · Yin Earth, late summer and Wood storage
Wei, wèi, is the eighth branch: yin, principal phase Earth, zodiac Goat, 13:00–15:00, with hidden Ji, Ding and Yi. It corresponds to late summer and completes the summer seasonal group with Si and Wu.
Wei combines with Wu, clashes with Chou and participates in the Hai–Mao–Wei Wood trine. Wei and Chou both place Ji Earth first in the hidden-stem list, but their other members and seasonal positions differ. Collapsing all four Earth branches into a single undifferentiated Earth count discards the distinctions this reference is meant to make readable.
Shen · Yang Metal, early autumn and hidden Water
Shen, shēn, is the ninth branch: yang, principal phase Metal, zodiac Monkey, 15:00–17:00, with hidden Geng, Ren and Wu. It corresponds to early autumn and opens the western seasonal group with You and Xu.
Shen combines with Si, clashes with Yin and joins Zi and Chen in the Water trine. Shen containing Ren is one membership fact; Shen–Zi–Chen forming a three-branch group is another. The first does not establish that all three branches are present. If only Shen and Zi occur, identify the missing Chen before discussing a partial group; do not call two symbols a complete three-member structure.
You · Yin Metal, west and midautumn
You, yǒu, is the tenth branch: yin, principal phase Metal, zodiac Rooster, 17:00–19:00, with hidden Xin. It corresponds to the west and midautumn, opposite Mao in the branch sequence.
You combines with Chen and joins Si and Chou in the Metal trine. A year with branch You is a Rooster year. A You hour, however, is a time period: it does not make everyone born during it a Rooster by year zodiac. Locate the symbol in the year, month, day or hour field before choosing which correspondence answers the question.
Xu · Yang Earth, late autumn and Fire storage
Xu, xū, is the eleventh branch: yang, principal phase Earth, zodiac Dog, 19:00–21:00, with hidden Wu, Xin and Ding. Xu is not the stem Wu; the second part of Jia Xu must be read as the branch name xū.
Xu corresponds to late autumn, clashes with Chen, combines with Mao and joins Yin and Wu in the Fire trine. Fire storehouse describes a storage relationship, not a claim that Xu contains nothing but Fire. Xu and Chen both place Wu Earth first, but their other hidden stems are Xin and Ding versus Yi and Gui. Shared yang Earth does not erase that difference.
Hai · Yin Water, early winter and hidden Wood
Hai, hài, is the twelfth branch: yin, principal phase Water, zodiac Pig, 21:00–23:00, with hidden Ren and Jia. It corresponds to early winter and forms the northern seasonal group with Zi and Chou. After Hai, the branch sequence returns to Zi.
Hai combines with Yin, clashes with Si and joins Mao and Wei in the Wood trine. A hidden Jia does not require every occurrence of Hai to be read as Wood. Likewise, the statement that Jia's Changsheng position is Hai needs to retain Jia as its reference. Saying simply that Hai means growth omits the stem-dependent half of the rule.
The sexagenary cycle: why the return takes sixty steps
Both sequences advance one place each step. After pair 60, both return to Jia Zi. Each ten-pair group leaves two branches unpaired.
Example 1: from Jia Zi to Jia Xu, then back to Jia Zi
Start with Jia and Zi together. One step gives Yi Chou; nine steps give Gui You. One more step returns the stem to Jia but takes the branch to Xu, giving Jia Xu. Stems return every 10 steps and branches every 12. Their first shared return takes 60 steps: lcm(10, 12) = 60.
This explains invalid pairs. Jia always meets an odd-position branch, never the even-position Chou. Multiplying 10 by 12 gives 120 arbitrary pairings, but arbitrary pairing is not the rule of this sequence. Both positions advance simultaneously. With traditional polarity labels applied, this becomes yang stem with yang branch and yin stem with yin branch.
Six xun and their two unoccupied branches
A xun contains ten pairs, starting with a Jia stem and continuing through Gui. Because there are twelve branches, only ten appear within any one xun. Its two remaining branches are the unoccupied or void branches. This is first a reproducible sequence structure. Divinatory interpretations of Xunkong or Kongwang add a separate layer; two unused positions do not establish that an undertaking will fail.
| First pair of the xun | Last pair | Two unoccupied branches |
|---|---|---|
| Jia Zi | Gui You | Xu, Hai |
| Jia Xu | Gui Wei | Shen, You |
| Jia Shen | Gui Si | Wu, Wei |
| Jia Wu | Gui Mao | Chen, Si |
| Jia Chen | Gui Chou | Yin, Mao |
| Jia Yin | Gui Hai | Zi, Chou |
For example, Bing Yin belongs to the Jia Zi xun, whose void branches are Xu and Hai. If a tool labels Xu void, ask which pillar's xun supplies the reference. Different applications can use different references. Wu Xing Da Yi, volume 1, on stem and branch numbers connects the ten stems and the xun; the table above can also be recomputed directly from the cycle.
Ordinary phase attributes and Nayin answer different questions
Jia Zi carries at least three different phase-related fields. Jia is Wood; Zi's principal phase is Water; and Jia Zi shares the Nayin label Haizhong Jin, Metal in the Sea, with Yi Chou. The first two describe individual symbols, while Nayin classifies paired designations. Before asking what phase Jia Zi is, specify which field you mean.
The sixty pairs form thirty two-pair Nayin groups. See Nayin Wuxing for their names and imagery. Nayin does not replace the individual stem and branch phases when deriving Ten Gods relationships. Historical explanations also involve musical pitches and numbers, as in Wu Xing Da Yi, volume 1, on Nayin numbers; these are not modern physical measurements.
Year, month, day and hour: boundaries before calculations
The same sixty labels can identify different time units. Year designations advance by years; day designations advance by days. A sexagenary cycle does not always mean sixty years. Below, lunar-calendar years use a lunar New Year boundary; Bazi year and month pillars use the stated Ziping solar-term convention, with Lichun starting the year and twelve jie instants starting the months. Hour pillars additionally require explicit day-boundary and time-basis settings.
Quick reference: year, month, day and hour boundaries
These rules distinguish calendar conventions from this site's BaZi settings. Before comparing tools, align the Gregorian date, clock time, UTC offset and solar-time setting. Apply the declared time convention consistently.
| Item | Boundary to establish | Worked reference |
|---|---|---|
| Stem–branch year and zodiac year | Our BaZi year pillar changes at the Lichun instant; the popular zodiac year often changes on lunar New Year's Day | Between Lichun and New Year in 2018 |
| Month pillar | Changes at the twelve opening Jie terms, not on lunar day one or at every middle term | Solar-month table |
| Day pillar | Our day pillar changes at 00:00 in the adopted time, not automatically at 23:00 | Continuous day sequence |
| Hour branch | Zi spans 23:00–00:59; each remaining branch spans two hours | Individual branch reference |
| Hour stem | At 23:00–23:59, our hour stem uses the next day's stem while the day pillar still belongs to the current day | Five Rats and late-Zi examples |
See the Hong Kong Observatory sources below for calendar years and solar terms. The midnight day boundary and late-Zi hour-stem rule describe this site's charting convention. Check the correction terms in the solar-time tool and worked examples.
Example 2: between Lichun and Lunar New Year in 2018
Consider February 10, 2018, at 12:00 in Hong Kong/Beijing standard time, without an apparent-solar-time correction. Lichun fell on February 4 that year; the first day of the first lunar month was February 16. The Observatory's 2018 daily conversion table identifies February 10 as day 25 of lunar month 12.
| Question | Boundary used | Result on this date |
|---|---|---|
| Which lunar-calendar year? | Midnight starting lunar month 1, day 1 | Still Ding You |
| Which Bazi year pillar here? | The Lichun instant | Already Wu Xu |
| Which lunar month? | The month beginning on its new-moon day | Month 12 |
| Which Bazi month pillar here? | Yin month from Lichun to Jingzhe; Wu years start Yin with Jia | Jia Yin |
Two year designations and two month descriptions coexist because they answer different questions. In What Year Is It Today?, the Observatory explicitly states its midnight lunar New Year boundary in Hong Kong standard time, while noting that some divinatory practices use Lichun. Apply the boundary to the actual date or instant instead of assigning every day in Gregorian 2018 to one lunar-calendar year.
Solar-term months and lunar months have different boundaries
Lunar months start on the day of a new moon and usually contain 29 or 30 days. The 24 solar terms divide solar longitude into 15-degree intervals. This guide's solar-term months are the twelve intervals below. Each includes its starting instant and ends when the next starts; neither a Gregorian month opening nor lunar day 1 substitutes for that instant.
| Month branch | Start → next start | Month branch | Start → next start |
|---|---|---|---|
| Yin | Lichun → Jingzhe | Shen | Liqiu → Bailu |
| Mao | Jingzhe → Qingming | You | Bailu → Hanlu |
| Chen | Qingming → Lixia | Xu | Hanlu → Lidong |
| Si | Lixia → Mangzhong | Hai | Lidong → Daxue |
| Wu | Mangzhong → Xiaoshu | Zi | Daxue → Xiaohan |
| Wei | Xiaoshu → Liqiu | Chou | Xiaohan → Lichun |
Each interval also contains a zhongqi, the intervening solar term: Yushui within Yin month, for example, and Chunfen within Mao month. The convention here changes the month at the jie, not the intervening zhongqi. The branch and seasonal discussions in San Ming Tong Hui, volume 2 provide traditional context; use astronomical data for modern exact transition times, not an ancient allocation of days within a month.
Example 3: immediately around a transition. Let T be a verified Jingzhe instant for a particular year and time zone. One minute before T remains Yin month; at T and afterwards, Mao month applies. If that year's Yin month is Jia Yin, the following month is Yi Mao even if lunar day 1 has not arrived. T represents an input that must be checked, not an invented fixed Gregorian clock time.
A leap lunar month does not create a thirteenth branch. Modern intercalation also considers the winter-solstice month and the number of months between successive winter-solstice months. “No zhongqi” alone is not a sufficient rule in every context. See the Central Weather Administration's explanation of leap-month placement.
Five Tigers: derive a month stem from a year stem
First establish the year stem and month branch under the selected boundary convention. The Five Tigers rule then supplies the month stem; it does not calculate Lichun. The table agrees with the Observatory's year–month stem table. Its traditional derivation verse appears in San Ming Tong Hui, volume 2, on deriving months and hours.
| Year stem | Yin month | Mao month | Chen month |
|---|---|---|---|
| Jia, Ji | Bing Yin | Ding Mao | Wu Chen |
| Yi, Geng | Wu Yin | Ji Mao | Geng Chen |
| Bing, Xin | Geng Yin | Xin Mao | Ren Chen |
| Ding, Ren | Ren Yin | Gui Mao | Jia Chen |
| Wu, Gui | Jia Yin | Yi Mao | Bing Chen |
Example 4: Chen month in a Ji year. Ji belongs to the Jia–Ji group, so start Yin month at Bing Yin. Advance to Ding Mao, then Wu Chen. The answer is Wu Chen. Do not start counting stems from Jia merely because Chen is branch number five: this method begins with the Yin month, whose starting stem depends on the year stem.
Day designations continue across months
The day count runs continuously around the sixty-pair cycle. If a day is established as Gui Hai, the next day is Jia Zi, regardless of a lunar-month, Gregorian-month or year boundary. Adding Gregorian year, month and day numbers and taking a final digit is not a reliable day-pillar method.
Example 5: crossing civil midnight. Suppose a civil date has been established as Yi You, and the chosen day-pillar boundary is 00:00. At 23:59 its day pillar remains Yi You; at 00:00 the next date becomes Bing Xu. This example starts from a known designation to demonstrate sequence continuity and a boundary. It is not a calendar for converting an arbitrary Gregorian date.
Five Rats and late Zi: separate the day pillar from the hour stem
Five Rats derives the Zi-hour stem from the selected day stem, then advances through the hour branches. It neither establishes the day's stem nor chooses a late-Zi convention on the reader's behalf.
| Day stem used for hour derivation | Zi hour | Chou hour | Yin hour |
|---|---|---|---|
| Jia, Ji | Jia Zi | Yi Chou | Bing Yin |
| Yi, Geng | Bing Zi | Ding Chou | Wu Yin |
| Bing, Xin | Wu Zi | Ji Chou | Geng Yin |
| Ding, Ren | Geng Zi | Xin Chou | Ren Yin |
| Wu, Gui | Ren Zi | Gui Chou | Jia Yin |
Example 6: Wu hour on a Gui day. The Wu–Gui group starts at Ren Zi. Continue through Gui Chou, Jia Yin, Yi Mao, Bing Chen and Ding Si to Wu Wu. The first Wu is the hour stem and the second is the hour branch. Identify the required branch, then advance six times from Zi; do not treat the clock number 12 in 12:00 as a stem index.
Example 7: why 23:30 can produce different pairs. Suppose the civil day is Yi You, the following day is Bing Xu and the hour branch is Zi. Two choices still matter: whether the day pillar changes at 23:00 or 00:00, and whether the hour stem uses the current or following day's stem.
| Explicit convention | Day pillar at 23:30 | Zi-hour pillar |
|---|---|---|
| Change day at 23:00; use the new day stem for the hour | Bing Xu | Wu Zi |
| Change day at 00:00; use the current day stem during late Zi | Yi You | Bing Zi |
| Change day at 00:00; use the following day stem during late Zi | Yi You | Wu Zi |
The third row describes this site's current Bazi dependency setting. These rows distinguish rule combinations; they are not an exhaustive taxonomy of every school. Saying that late Zi does not change the day is insufficient without also stating the day stem used for the hour. The third result is not, on its own, an error in Five Rats.
- 1Bing Yin
- 2Ding Mao
- 3Wu Chen
- 4Ji Si
- 5Geng Wu
- 6Xin Wei
- 7Ren Shen
- 8Gui You
- 9Jia Xu
- 10Yi Hai
- 11Bing Zi
- 12Ding Chou
Start with the Yin month and move the stem forward once per month. In the Ziping month pillar, months change at the relevant solar-term boundary, not the lunar month's first day.
Reference tables: Hong Kong ObservatoryExample 8: apparent solar time can change the hour branch
Civil standard time follows a time zone. Local mean solar time adds a longitude correction; local apparent solar time also adds the equation of time. Here the sign convention is explicitly equation of time = apparent solar time minus mean solar time, so apparent solar time = standard time + longitude correction + equation of time. One degree of longitude corresponds to about four minutes: add eastward, subtract westward. The Central Weather Administration's time classifications explain the concepts. Its equation-of-time page uses the opposite difference sign; check the definition before transferring a numerical value between sources.
For a hypothetical arithmetic exercise, assume no daylight saving, standard time 09:10, a standard meridian of 120°E, a location at 116°E and an equation of time of −5 minutes under the definition above. The longitude correction is −16 minutes, giving local mean solar time 08:54. Subtract another five minutes for apparent solar time 08:49. The civil clock corresponds to Si hour; the corrected apparent solar time corresponds to Chen hour.
The −5 minutes is an exercise input, not an observed value for a specified birthday. A real conversion needs the date, location, historical time zone, daylight-saving status and that date's equation of time, with any date crossing recorded. Convert daylight-saving clock time back to standard time first; do not subtract the same offset twice.
Relationships: identify the structure, then its conditions
These are group memberships, not automatic transformation or predictions. Read the conditions and sources below.
Read all groups and their conditionsGeneration, control and the Ten Gods need a reference
The traditional generating cycle is Wood → Fire → Earth → Metal → Water → Wood. The controlling cycle is Wood → Earth → Water → Fire → Metal → Wood. These relations are recorded in the generation and control discussions of Wu Xing Da Yi, volume 2. The everyday analogies used to explain them belong to that classification system, not to a universal modern chemical reaction model.
The Ten Gods, or Shishen, then select the day stem as the reference self and distinguish both phase relation and polarity. This guide uses the common Ziping names below. Older texts also use names such as Daoshi, Xiao and Baicai, with context affecting their meaning. The opening discussion of relationship names and the individual finance, officer, resource and output chapters in San Ming Tong Hui, Siku Quanshu version, volume 5 provide day-stem-based examples. This introductory table does not compress every historical qualification of those names into one rule.
| Other stem relative to the day stem | Same polarity | Opposite polarity | Examples with Jia as reference |
|---|---|---|---|
| Same phase | Bijian: Companion | Jiecai: Rob Wealth | Jia, Yi |
| Generated by the reference | Shishen: Eating God | Shangguan: Hurting Officer | Bing, Ding |
| Controlled by the reference | Piancai: Indirect Wealth | Zhengcai: Direct Wealth | Wu, Ji |
| Controls the reference | Qisha / Pianguan: Seven Killings / Indirect Officer | Zhengguan: Direct Officer | Geng, Xin |
| Generates the reference | Pianyin: Indirect Resource | Zhengyin: Direct Resource | Ren, Gui |
Rizhu, or Day Master, names the role selected as the reference. Bijian names a relationship to that reference. A chart may therefore label the day-stem position Day Master and another occurrence of the same stem Companion. Words such as wealth, officer and killings are technical labels here, not verified financial, career or harm events.
Five stem combinations: pairing and transformation are separate
| Combining stems | Phase named in traditional transformation discussion |
|---|---|
| Jia, Ji | Earth |
| Yi, Geng | Metal |
| Bing, Xin | Water |
| Ding, Ren | Wood |
| Wu, Gui | Fire |
The pairings and transformation directions appear in the separate stem-combination and transformation chapters of San Ming Tong Hui, volume 2. The separation matters: identifying members is one operation, while transformation adds seasonal and contextual conditions. The diagram here records a combination; it does not turn every Wood and Earth attribute into Earth merely because Jia and Ji appear together.
Historical marriage analogies explain these relations within their period's symbolism; they do not establish present-day romantic compatibility. Some systems also list Jia–Geng, Yi–Xin, Bing–Ren and Ding–Gui as stem clashes. The term Chongpo has a broader scope in Wu Xing Da Yi, so a four-pair stem-clash definition needs an explicit convention rather than an assertion that every classical text uses it.
Liuhe: six branch combinations
The six pairs are Zi–Chou, Yin–Hai, Mao–Xu, Chen–You, Si–Shen and Wu–Wei. They cover all twelve branches, each with one partner in this table. Cross-check the members in the branch-combination chapter of San Ming Tong Hui, volume 2 and the combination discussion in Wu Xing Da Yi, volume 2.
Recognizing Zi–Chou requires checking two members. Discussing a transformation phase, whether transformation occurs, priority over another relation or the whole chart's interpretation requires further rules from a specified tradition. This guide does not present one Liuhe transformation table as universal, or translate combination into a claim about naturally compatible zodiac partners.
Liuchong: six opposite positions on the branch circle
The six clash pairs are Zi–Wu, Chou–Wei, Yin–Shen, Mao–You, Chen–Xu and Si–Hai. On a circle with twelve equally spaced branches, the members are six steps apart. The traditional expression that a branch clashes with the seventh position counts the starting branch as position one; it is consistent with a six-step separation.
The pair table appears in the Chongpo chapter of Wu Xing Da Yi, volume 2. Circular geometry helps remember the members; it is not evidence of real-world causation. A relation diagram does not establish the occurrence or probability of a job loss, relationship separation or illness.
Sanhe, partial trines and Gong: state which member is missing
| Three-branch group | Associated phase | Three positions in this explanation |
|---|---|---|
| Shen, Zi, Chen | Water | Growth, peak, storage |
| Hai, Mao, Wei | Wood | Growth, peak, storage |
| Yin, Wu, Xu | Fire | Growth, peak, storage |
| Si, You, Chou | Metal | Growth, peak, storage |
The Sanhe chapter of San Ming Tong Hui explains the three positions through growth, peak and storage, and warns against treating a missing member as a complete transformed group. A group name does not rewrite every member's principal phase. Even complete membership is separate from the additional transformation conditions used by a tradition.
For this guide's teaching terminology, two members including the peak branch form a partial trine, or Banhe: Shen–Zi or Zi–Chen, for example. Growth and storage members without the peak are called Gong: Shen–Chen framing the absent Zi. Other authors may use the terms differently. The diagram shows all three members of a full Sanhe group; naming Shen–Chen as Gong does not insert an actual Zi into the four pillars.
Sanhui: three successive branches of a season
Here Sanhui, or seasonal assembly, means Yin–Mao–Chen for eastern Wood, Si–Wu–Wei for southern Fire, Shen–You–Xu for western Metal, and Hai–Zi–Chou for northern Water. Each collects three successive seasonal branches. The directional memberships can be checked in the mixed-direction discussion of Wu Xing Da Yi, volume 2.
Yin–Mao–Chen and Hai–Mao–Wei both have a Wood association, but the first is a spring-season sequence and the second a growth–peak–storage trine. They are not interchangeable. Chen retains its principal Earth phase while belonging to the eastern seasonal group. A line joining three members displays a correspondence; it does not assert that every occurrence automatically transforms into one phase.
Liuhai: six harm pairs, checked through combinations and clashes
The six pairs are Zi–Wei, Chou–Wu, Yin–Si, Mao–Chen, Shen–Hai and You–Xu. They appear in the harm discussions of Wu Xing Da Yi and San Ming Tong Hui. Those discussions also explain members through combination and clash partners: Zi combines with Chou while Wei clashes with Chou, providing one memory path to Zi–Wei harm.
This explanation does not establish that people with the corresponding year animals will harm each other. Harm is a traditional relation name; real interpersonal judgments need actual behavior. A branch can participate in several kinds of relation, so one harm line should not replace the rest of the chart's structure.
Po: specify which text's meaning of break is intended
The term break needs especially careful attribution. In its Chongpo chapter, Wu Xing Da Yi, volume 2 discusses opposing stems and branches; its branch pairs match the six clashes. This is not the separate six-break table often found in modern reference lists.
The Posha passage reproduced in Gu Jin Tu Shu Ji Cheng, Arts section, volume 601 lists Mao–Wu, Chou–Chen, Zi–You and Wei–Xu, while excluding the four seasonal-opening branches from that list. This guide's break diagram displays only those four Posha pairs. A generic appeal to ancient rules cannot validate every modern six-break table; nor is this four-pair table presented as the one universal definition of six breaks.
Xing: groups, pairs and self-punishment
Members and directions can be checked against the punishment chapters of Wu Xing Da Yi, volume 2 and San Ming Tong Hui.
| Structure | Form shown here | Distinction to retain |
|---|---|---|
| Yin–Si–Shen group | Yin → Si → Shen → Yin | Two present members are not the same as all three |
| Chou–Xu–Wei group | Chou → Xu → Wei → Chou | Do not silently turn every directional permutation into the same rule |
| Zi–Mao pair | Zi ↔ Mao | A two-branch relation does not require a third member |
| Self-punishment | Chen, Wu, You or Hai repeated with itself | Four separate repeated-branch patterns, not all four punishing one another |
Traditions differ over when to apply a punishment interpretation, whether full group membership is needed and what additional conditions matter. This guide lists structures without a two-symbol disaster trigger. San Ming Tong Hui itself warns against treating every occurrence of Xing as unfavorable; a relation name and a concrete judgment must be read separately even within historical texts.
Twelve stages: whose position is being described?
The twelve names run Changsheng, Muyu, Guandai, Linguan, Diwang, Shuai, Bing, Si, Mu, Jue, Tai and Yang, then repeat. They borrow life-process imagery: growth, bathing, dressing, office, peak, decline, sickness, death, tomb, extinction, gestation and nurturing. A chart label is not a medical or lifespan finding. The twelve-palace discussion in San Ming Tong Hui, volume 2 lists the stages and cautions against reading growth and peak as invariably favorable, or death and extinction as invariably unfavorable.
The Twelve Life Stages entry carries the complete ten-stem table, the source texts for both direction conventions and the exact scope of their disagreement, the four classical arrangements for Earth, and a comparison of how BaZi, Zi Wei, Liu Yao and Qi Men each start the sequence.
Application requires a stem reference and a direction rule. The text places Jia's Changsheng at Hai, Bing's at Yin, Geng's at Si and Ren's at Shen; yin stems use different starts and direction. Earth also has differing arrangements: the stem discussion in this text follows Bing for Wu and Ding for Ji. Alternating between a five-phase table and a ten-stem polarity table without stating the switch will not give consistently defined results.
Applications, exercises and further reading
How different systems use the same symbols
| Setting | What Ganzhi helps identify | What cannot simply be transferred |
|---|---|---|
| Everyday calendars | Year names, day sequence, zodiac and two-hour periods | A calendar label alone does not supply a divinatory judgment |
| Bazi | Four time pillars and relationships to a day-stem reference | A zodiac animal or Nayin label does not replace the four pillars |
| Ziwei Doushu | Branch-labeled palaces and birth-related chart inputs | A palace branch is not necessarily a Bazi month branch |
| Liuyao | Najia assignments, month and day references | A line is not interchangeable with a person's Day Master |
| Qimen Dunjia | Stem placement, timing and xun structures | Shared stem names do not justify importing Bazi Ten Gods conclusions |
| Meihua Yishu | Year-branch and date/time values in some time-based methods | Its different casting methods do not all reduce to one Ganzhi algorithm |
These are reading entry points, not replacements for each system's own rules. The shared habit is to identify a symbol's position and reference, then determine whether the current discussion concerns calendars, traditional classification or a divinatory procedure.
Reading the 2018 example from inputs to limits
Return to February 10, 2018, at 12:00. First specify Hong Kong/Beijing standard time without an apparent-solar-time correction. The official calendar gives lunar month 12, day 25. Under the lunar New Year boundary, it remains Ding You year. Under this guide's Bazi year and month convention, Lichun has passed, so the year pillar is Wu Xu and the month branch Yin. Five Tigers starts a Wu year's Yin month at Jia, producing Jia Yin.
The ordinary clock table places 12:00 in Wu hour. This does not yet justify deriving the hour stem from the year stem Wu: Five Rats needs a checked day stem. Recognizing that missing input is part of a complete explanation. A reader should know what the available evidence establishes and which input is still required to finish the four pillars.
Three checks for keeping the layers separate
- What follows Gui You? Jia Xu. The stem returns to Jia while the branch advances from You to Xu; this is not their shared restart.
- Should Zi's yang label or hidden Gui's yin label be changed? Neither. They classify different objects. Identify the field's referent first.
- Can Shen–Chen supply an actual Zi to complete the Water trine? No. This guide calls the missing-peak structure Gong, but a relationship name cannot add a symbol that is not present.
For memorization, learn the two sequences first, then the five stem-phase pairs and the six opposing branch pairs. Use those coordinates to look up combinations and trines. Five Tigers starts Yin month with Bing, Wu, Geng, Ren or Jia for the five year-stem groups in order; Five Rats starts Zi hour with Jia, Bing, Wu, Geng or Ren for the corresponding day-stem groups. Run a full example after learning the starting names so that both the starting point and the step count are clear.
Sources: separate recorded rules from predictive statements
Official astronomical material is suitable for sequences, solar terms and Gregorian–lunar date conversion. Historical texts establish traditional classifications and a particular text's terminology. The linked Wu Xing Da Yi, San Ming Tong Hui and Yuan Hai Zi Ping pages are identifiable electronic texts with named sections, not a claim that every underlying scanned edition has been fully collated. Similar-looking characters, alternative names and version differences still require context; the hidden-stem section specifically notes its source limitation.
Historical works also contain social hierarchies, personality claims and predictions about health or fortune. Citing a pair table does not endorse those statements as modern facts. For a personal chart, record the time, place and chosen conventions. For a term, return to the relevant section and source. This September 8, 2026 edition concentrates on sequence structure, relationship definitions and time boundaries; later textual revisions should retain their evidence and explain what changed.
FAQ
- What are the ten stems and twelve branches?
- The stems are Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren and Gui. The branches are Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu and Hai. Each pair places its stem first.
- Why are there sixty pairs rather than 120?
- Both sequences advance one position at a time. The least common multiple of 10 and 12 is 60. Odd positions only meet odd positions and even positions only meet even positions, so Jia Chou and Yi Zi do not occur.
- How do I pronounce Gui, Si and Xu?
- Their tone-marked pinyin is guǐ, sì and xū. The stem Wu is wù, while the branch Wu is wǔ. Plain pinyin can conceal this distinction, so check whether a label denotes a stem or a branch.
- Are Ganzhi and the animal zodiac the same thing?
- No. Each zodiac animal corresponds to a branch. A year animal identifies the year branch but not its stem, and it cannot supply all four pairs of a Bazi chart.
- Can a yin stem pair with a yang branch?
- Not in the standard sixty-pair sequence. Alternating yin and yang labels stay aligned as the two sequences advance together. This is a rule about sequence positions, not a rule about people's genders.
- Why does yang Zi contain yin Gui?
- The branch's yin–yang label and its hidden stem's label describe different objects. Zi is a yang branch; the hidden-stem table lists Gui, a yin stem. Neither field needs to be changed.
- Do hidden stems have universal percentages?
- No universal percentages are assigned here. Membership, display order, seasonal day allocations and an application's numerical weights are different things. This guide lists members with the principal stem first.
- Does the Ganzhi year change at Lunar New Year or Lichun?
- State the purpose first. The Hong Kong Observatory changes the lunar-calendar year designation at midnight on the first day of the first lunar month, in Hong Kong standard time. The Ziping solar-term convention explained here changes the year pillar at Lichun.
- Is Lichun always midnight on February 4?
- No. Lichun is the instant at which the Sun's ecliptic longitude reaches 315 degrees. Check the year-specific date, time and time zone instead of substituting a fixed midnight.
- Does a Bazi month change on the first lunar day?
- Under this guide's Ziping convention, the month pillar changes at twelve jie boundaries, including Lichun and Jingzhe. A lunar month begins on its new-moon day, so these boundaries often differ.
- Does a leap month add a thirteenth branch?
- No. Intercalation belongs to the lunisolar calendar. The branch sequence still has twelve members, and a leap lunar month does not create an extra solar-term month.
- Does the day cycle restart with Jia Zi every month?
- No. Day designations continue through the sixty-pair cycle across month and year boundaries. Converting an arbitrary calendar date still requires a checked calendar or a validated algorithm with a reference date.
- What hours does Zi cover?
- The usual modern clock correspondence is 23:00 to 01:00. It spans civil midnight. The day-pillar boundary and the choice of day stem used to derive the hour stem must still be specified separately.
- What do Five Tigers and Five Rats derive?
- Five Tigers derives the Yin-month stem from the year stem. Five Rats derives the Zi-hour stem from the selected day stem. Neither method calculates solar-term instants or establishes the day's Ganzhi designation.
- Is Beijing time the same as apparent solar time?
- No. Beijing time is civil standard time. Local mean solar time requires a longitude correction; local apparent solar time also requires the equation of time. Historical daylight-saving adjustments must be handled without counting the same offset twice.
- Is Jia Zi Wood, Water or Metal?
- Jia is Wood, Zi's principal phase is Water, and the Jia Zi pair has the Nayin label Haizhong Jin, or Metal in the Sea. These are three different fields, not competing answers to one precisely defined question.
- Does a stem combination automatically transform?
- No. A pair table identifies members. Traditional transformation discussions add seasonal and contextual conditions. This guide does not automatically replace both original phases with the transformation phase.
- How do Sanhe and Sanhui differ?
- Sanhe groups, such as Shen–Zi–Chen, connect branches four positions apart. Sanhui groups, such as Yin–Mao–Chen, collect three successive seasonal branches. Their members and explanatory frameworks differ.
- Do clashes, punishments, harms or breaks predict bad events?
- No. These are traditional relation names. Identifying one does not establish a future illness, relationship outcome or lifespan. Even the word break has different meanings in different texts.
- Is Ganzhi enough to interpret a whole chart?
- It is a foundation for reading symbols. Each system also requires its own timing rules, reference points and interpretive conventions. First establish how a result was derived and what its labels refer to.
References
- Hong Kong Observatory: Heavenly Stems and Earthly Branches
- Central Weather Administration: the Ganzhi cycle
- Hong Kong Observatory: What Year Is It Today?
- Hong Kong Observatory: the 24 Solar Terms
- Hong Kong Observatory: 2018 Gregorian–lunar conversion table
- Wu Xing Da Yi, volume 1: names and numerical structures, electronic text
- Wu Xing Da Yi, volume 2: correspondences and relations, electronic text
- San Ming Tong Hui, volume 2: timing and relations, electronic text
- Yuan Hai Zi Ping: hidden-stem verse, electronic text with source warning
- San Ming Tong Hui, Siku Quanshu version, volume 5: relationship categories and mixed qi
- Gu Jin Tu Shu Ji Cheng, Arts section, volume 601: Posha, electronic text